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We explore the behavior of the iterative procedure to obtain the solution tothe gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily largevalues of the coupling constant and in the presence of a magnetic field and athermal bath. We find that the iterative procedure shows a different behaviordepending on the regularization scheme used. It is stable and very accuratewhen a hard cut-off is employed. Nevertheless, for the Paul-Villars and propertime regularization schemes, there exists a value of the coupling constant(different in each case) from where the procedure becomes chaotic and does notconverge any longer.

Solving the Gap Equation of the NJL Model through Iteration: Unexpected Chaos